The polynomials $f(x)$ and $g(x)$ are given by $f(x) = 4x^3 + ax^2 + 8x + 15$ and $g(x) = x^2 + bx + 18$, with $a$ and $b$ as constants.
(a)[2]
Given that $(x + 3)$ is a factor of $f(x)$, determine the value of $a$.
(b)[2]
Given that the remainder is $40$ when $g(x)$ is divided by $(x - 2)$, determine the value of $b$.
(c)[3]
When these values of $a$ and $b$ are used, completely factorise $f(x) - g(x)$.
(d)[3]
Hence solve the equation $f(\cosec \theta) - g(\cosec \theta) = 0$ for $0 < \theta < 2\pi$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x=-3$, make the expression equal to zero and try to solve for $a$” …